Kolmogorov-Smirnov test for Student distribution

Description

Performs Kolmogorov-Smirnov goodness-of-fit test for the hypothesis that the sample comes from a Student's t-distribution. The statistic compares the empirical distribution function with the theoretical Student cumulative distribution function.

Hypothesis of Student Distribution The null hypothesis is that the data comes from a Student's t-distribution with positive degrees of freedom df, location parameter loc, and positive scale parameter scale.

Test Statistic The statistic is based on the maximum distance between the empirical distribution function and the reference Student cumulative distribution function.

Usage

from pysatl_criterion.statistics.goodness_of_fit import (
    KolmogorovSmirnovStudentGofStatistic,
)


test_statistic = KolmogorovSmirnovStudentGofStatistic(df=5, loc=0, scale=1)
statistic_result = test_statistic.execute_statistic([-1.8, -0.9, -0.25, 0.0, 0.31, 0.95, 1.7])
print(statistic_result)

Arguments

df - positive degrees of freedom of the Student's t-distribution. Default value is 1.

loc - location parameter of the Student's t-distribution. Default value is 0.

scale - positive scale parameter of the Student's t-distribution. Default value is 1.

alternative_type - alternative hypothesis type used by the Kolmogorov-Smirnov statistic.

rvs - array-like sample data passed to execute_statistic.

Details

The implementation standardizes the ordered observations as

\[ Z_i = \frac{X_{(i)} - loc}{scale} \]

and evaluates the Student CDF with df degrees of freedom.

Author(s)

Dmitriy Rusanov, Alexey Mironov

References

Kolmogorov, A.N. (1933): Sulla determinazione empirica di una legge di distribuzione. - Giornale dell'Istituto Italiano degli Attuari, vol. 4, pp. 83-91.

Smirnov, N.V. (1948): Table for estimating the goodness of fit of empirical distributions. - Annals of Mathematical Statistics, vol. 19, pp. 279-281.

Examples

from pysatl_criterion.statistics.goodness_of_fit import (
    KolmogorovSmirnovStudentGofStatistic,
)


test_statistic = KolmogorovSmirnovStudentGofStatistic(df=5, loc=0, scale=1)
statistic_result = test_statistic.execute_statistic([-1.8, -0.9, -0.25, 0.0, 0.31, 0.95, 1.7])
print(statistic_result)